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Go to the National or TI websites and locate a datasheet for an operational amplifier. They will have reference schematics. It is not something most of us have lying around anymore since we all use IC amplifiers and fuhgeddaboudit.
With few exceptions, most ICs from the simplest logic gate to complex microprocessors are based upon discrete circuit designs and have ancestors in modular circuit board form. Up until the 1960's, before Kilby introduced the IC and when vacuum tubes were still common and transistors were in their infancy, common circuits like op-amps and timers were built in modular form for ease of assembly and system design. But they were all discrete components on a board. When the IC was invented, it was the next logical step to miniaturize these standard circuits onto the IC.
Even complex circuits like microprocessors, while a chip with a billion transistors has no pre-IC counterpart, it is still based upon the same building block nature of discrete circuits of the past.
You obviously can build your own op-amp,but it's cheaper to buy an IC, you have got to decide what you're going to use it for,before designing it,just for example;say you want to build a PWM,then look at the data sheet for the LM324N,it will show you 4 transistors,each with a different function,ie; comparitor, 12v reference,ect;this 14 pin chip.together with various resistors and diodes,would serve as the driver for a Mosfet,simple & cheap to populate on a small board.I pay around 50 cents for an IC,there are hundreds to choose from,whether you are building a stereo amp or any thing that requires the function of an intergrated circuit.(if you want to know anything ask Audioguru)